{"uid":"cap_Whc4bJgSDDKjctqDK9dzT","slug":"little-s-law-systems-capacity-calculator-761a2660","name":"Little's Law Systems Capacity Calculator","description":"Little's law L = rate x time in system: solve for concurrency, throughput or latency given any two; sizes pools.","url":"https://data-calc.x402tookit.com/littles-law?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":[],"properties":{"timeUnit":{"type":"string","description":"Unit of timeInSystem: ms, s (default), min or h"},"arrivalRate":{"type":"number","description":"Throughput lambda: items entering (and leaving) per second"},"timeInSystem":{"type":"number","description":"Average time W an item spends in the system (use timeUnit)"},"itemsInSystem":{"type":"number","description":"Average number L of items in the system (concurrency, connections, queue plus service)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"timeUnit":{"type":["null","string"]},"solvedFor":{"type":["null","string"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"itemsInSystem":{"type":["null","number"]},"timeInSystemInUnit":{"type":["null","number"]},"timeInSystemSeconds":{"type":["null","number"]},"arrivalRatePerSecond":{"type":["null","number"]},"poolSizeAt50PercentUtilization":{"type":["null","number"]},"poolSizeAt70PercentUtilization":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_bC3dN33c--hH8CQDQR5k_","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Applies Little's Law (L = λW) to solve for concurrency, throughput, or latency given any two of the three, and computes recommended pool sizes.","exampleAgentPrompt":"My API handles 200 requests per second and each request takes about 150 milliseconds on average — use Little's Law to tell me how many concurrent connections I need in flight at any time, and what connection pool size I should target at 70% utilization.","exampleUseCases":[{"title":"Database connection pool sizing","prompt":"My service sends 50 queries per second to the database and each query takes around 80ms to complete — figure out using Little's Law how many concurrent database connections are needed, and what pool size I should set at 70% utilization."},{"title":"API throughput from concurrency and latency","prompt":"I have a thread pool that keeps exactly 40 requests in flight at any time, and my average response latency is 250ms — solve Little's Law to tell me what throughput in requests per second that translates to."},{"title":"Latency estimation from concurrency and RPS","prompt":"My load balancer shows about 120 concurrent requests in flight during peak, and we're processing 600 requests per second — use Little's Law to calculate the average time each request spends in the system, in milliseconds."}],"resultDescription":"Returns the solved value of whichever Little's Law variable was omitted (concurrency L, throughput λ, or latency W), plus recommended connection/thread pool sizes at 50% and 70% utilization, a human-readable summary and verdict, and metadata including the time unit used and which variable was solved for.","failureModes":["All three parameters provided — endpoint cannot determine which to solve for","No parameters or only one parameter provided — underspecified, cannot solve","Non-numeric or negative values for rate, time, or concurrency — validation error","Invalid timeUnit value outside ms/s/min/h — parameter rejected","Payment not included or insufficient — 402 Payment Required response"],"whenToPreferThis":"Use this endpoint when you need a quick, correct application of Little's Law to size concurrency, compute throughput, or derive latency for any queuing system — thread pools, connection pools, API gateways, or message queues — without writing the math yourself. Prefer this over general-purpose calculators or LLM arithmetic when you need authoritative pool-size recommendations (50% and 70% utilization targets) alongside the solved variable.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T00:35:32.885Z","isFirstParty":false,"canonicalSlug":"little-s-law-systems-capacity-calculator-761a2660"}